Abstract
The distribution of ticks is essentially determined by the presence of climatic conditions and ecological contexts suitable for their survival and development. We build a model that explicitly takes into account each physiological state through a system of infinite differential equations where tick population density are structured on an infinite discrete set. We suppose that intrastage development process is temperature dependent (Arrhenius temperatures function) and that larvae hatching and adult mortality are temperature and water vapor deficit dependent. We analysed mathematically the model and have explicit the \(R_0\) of the tick population.
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Acknowledgements
The work was funded by the Laboratoire d’épidémiologie des infections enzootiques des herbivores en Tunisie: application à la lutte (LR16AGR01) (Ministère de l’enseignement supèrieure et de la recherche scientifique, Tunisie), the laboratory of Bioinformatic, biomathematics et biostatistics (LR16IPT09) (Ministère de l’enseignement supérieur et de la recherche scientifique, Tunisie) and was partly supported by the CGIAR Research Program on Livestock from the International Center for Agricultural Research in the Dry Areas (ICARDA). The Departement de Mathematiques of UADB provides travel grant that contribute to realize this work. SBM and PIN acknowledge the Director, Pr Alassane Sy, the dean department, Dr Abdoul Aziz Fall of UFR SATIC and Pr Henda el Fekih of ENIT who facilitate their collaboration and scientific visits. We would like to thank the associate editor and the reviewer for their comments which greatly improved the reading of the manuscript. We would like also to thank reviewers of the first version of this manuscript that advise us to split our work in two, in order to improved the reading.
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Ndongo, M.S., Ndiaye, P.I., Gharbi, M. et al. A climate-based model for tick life cycle: positive semigroup theory on Cauchy problem approach. J. Math. Biol. 84, 52 (2022). https://doi.org/10.1007/s00285-022-01755-x
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DOI: https://doi.org/10.1007/s00285-022-01755-x
Keywords
- Differential equation model
- Ticks life-cycle model
- Basic reproduction number
- Tick life-cycle growth model
- Positive operators
- Spectral theory
- Quasi-compactness
- Temperature
Mathematics Subject Classification
- 92-10
- 47A13
- 47B65
- 34C60